Problem: Simplify the following expression: $ t = \dfrac{x - 10}{-6x} + \dfrac{9}{10} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{x - 10}{-6x} \times \dfrac{10}{10} = \dfrac{10x - 100}{-60x} $ Multiply the second expression by $\dfrac{-6x}{-6x}$ $ \dfrac{9}{10} \times \dfrac{-6x}{-6x} = \dfrac{-54x}{-60x} $ Therefore $ t = \dfrac{10x - 100}{-60x} + \dfrac{-54x}{-60x} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{10x - 100 - 54x}{-60x} $ $t = \dfrac{-44x - 100}{-60x}$ Simplify the expression by dividing the numerator and denominator by -4: $t = \dfrac{11x + 25}{15x}$